The alpha to gamma transition in Cerium: a theoretical view from optical spectroscopy

Kristjan Haulea,b and Gabriel Kotliarb

aJožef Stefan Institute, Ljubljana, SloveniabDepartment of Physics and Center for Material Theory, Rutgers University, Piscataway, NJ, USA

Classical theories of alpha to gamma phase Classical theories of alpha to gamma phase transitiontransition

estimated TK(exp)=2000K estimated TK(exp)=60-80K

4f

5d

6s

orb

ital

ly r

eso

lved

"fa

t" o

pti

cs

fo

r al

ph

a p

has

eL

DA

co

mp

ared

to

LD

A+

DM

FT

ff contribution to optics <<fd<<ddff contribution to optics <<fd<<dd

ConclusionsConclusionsThe main features of the optical spectra in Cerium are a consequenceThe main features of the optical spectra in Cerium are a consequence of a different hybridization strengthof a different hybridization strength

betweenbetween f f and and spdspd orbitals in orbitals in the two phasesthe two phasesKondo peak in low T alpha phase appears due to hybridization with Kondo peak in low T alpha phase appears due to hybridization with spspdd bands bandsOptics conductivity has mostly d characterOptics conductivity has mostly d character Optics shows Optics shows a narrow Drude peak, a narrow Drude peak, hybridization hybridization ((pseudopseudo))gap gap and mid infrared peak at 1eV and mid infrared peak at 1eV in alpha phasein alpha phase Optics in gamma phase show Optics in gamma phase show a a broad Drude like response (of d bands only)broad Drude like response (of d bands only)""KKondo volume collapseondo volume collapse model model"" explains the Cerium properties explains the Cerium properties better than better than the "the "MMott transition"ott transition" scenario scenario

TCA

Luttinger Ward functionallocal (eigen)state - full atomic base

, where

general AIM:

( )

two band Hubbard model, Bethe lattice, U=4D

three band Hubbard model, Bethe lattice,

U=5D, T=0.0625D

three band Hubbard model, Bethe lattice, U=5D, T=0.0625D

Using a novel approach to calculate optical properties of strongly correlated systems, we address the old question of the physical origin of the alpha to gamma transition in Cerium. We find that the Kondo collapse model, involving both the f and the spd electrons, describes the optical data better than a Mott transition picture involving the f electrons only. Our results compare well with existing experiments on thin films. We predict the full temperature dependence of the optical spectra and find the development of a hybridization pseudogap in the vicinity of the alpha to gamma phase transition.

Using a novel approach to calculate optical properties of strongly correlated systems, we address the old question of the physical origin of the alpha to gamma transition in Cerium. We find that the Kondo collapse model, involving both the f and the spd electrons, describes the optical data better than a Mott transition picture involving the f electrons only. Our results compare well with existing experiments on thin films. We predict the full temperature dependence of the optical spectra and find the development of a hybridization pseudogap in the vicinity of the alpha to gamma phase transition.

solution AIM

DMFT SCC

local in localized LMTO base

Impurity problem (14x14):

Impurity solvers (expansion in hybridization strength)Impurity solvers (expansion in hybridization strength)Impurity solvers (expansion in hybridization strength)Impurity solvers (expansion in hybridization strength)

•Mott transition (B. Johansson, 1974):Mott transition (B. Johansson, 1974):

Hubbard modelHubbard model

changes and causes Mott tr.changes and causes Mott tr.

•Kondo volume colapse (J.W. Allen, R.M. Martin, 1982):Kondo volume colapse (J.W. Allen, R.M. Martin, 1982):Anderson (impurity) modelAnderson (impurity) model

changes changes →→ chnange of T chnange of TKK

bath either constant or

taken from LDA and rescaled

ab initio calculationab initio calculation

contains tcontains tffff and V and Vfdfd hopping hopping

is self-consistently determinedis self-consistently determinedbath for AIMbath for AIM

Kondo volume colapse model resembles DMFT picture:Kondo volume colapse model resembles DMFT picture:

Solution of the Solution of the Anderson impurity model → Kondo physicsAnderson impurity model → Kondo physics

DifferenceDifference: : with DMFT the lattice problem is solved (and therefore with DMFT the lattice problem is solved (and therefore Δ must self-consistently determined) while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.)

LDA+DMFTLDA+DMFT

NCA

OCA

TCA

Tests of the impurity solverTests of the impurity solverTests of the impurity solverTests of the impurity solver•Quasiparticle renormalization amplitude•Quasiparticle renormalization amplitude •Imaginary axis data•Imaginary axis data

•Real axis data•Real axis data

Electron configuration of Ce

Atom : [Xe]4f25d06s2

Solid or compounds :

trivalent [Xe]4f1(5d6s)3,

tetravalent [Xe]4f0(5d6s)4

promotional model promotional model

(Ramirez, Falicov 1971)(Ramirez, Falicov 1971)•Transition is 1.order•ends with CP very similar to gas-liquid condesation

Various phases :

isostructural phase transition (T=298K, P=7kbar)

(fcc) phase

[ magnetic moment

(Curie-Wiess law),

large volume,

stable high-T, low-p]

(fcc) phase

[ loss of magnetic

moment (Pauli-para),

smaller volume,

stable low-T, high-p]

with large

volume collapse

v/v 15

35.2Å334.4Å324.7Å328Å3

LDA+ULDAexp.volumes

fermionic bathfermionic bath

mappingmapping

LDA+DMFT formalismLDA+DMFT formalismLDA+DMFT formalismLDA+DMFT formalism

LDA+DMFT results: PhotoemissionLDA+DMFT results: Photoemission

Optics calculation within LDA+DMFTOptics calculation within LDA+DMFT

LDA+DMFT results: OpticsLDA+DMFT results: Optics

•comparison to experimentcomparison to experiment •partial density of statespartial density of states

•temperature dependence of optics temperature dependence of optics (developement of a hybridization pseudogap)(developement of a hybridization pseudogap)